Comparing gravitational field strengths via graph slopes

Steps:

• Recognize that gravitational field strength $g$ equals the slope of a weight vs. mass graph, since weight $W = mg$.
• Examine the graph for planet X: steeper slope indicates higher $g$.
• Examine the graph for planet Y: shallower slope, one-third as steep as X's.
• Conclude $g_X = 3g_Y$ from the slope ratio.

Why D is correct:

• Gravitational field strength is the acceleration due to gravity, given by $g = W/m$, so the slope ratio directly shows $g_X$ is three times $g_Y$.

Why the others are wrong:

• A: Graphs allow direct comparison via slopes.
• B: Slopes differ, so $g$ values are unequal.
• C: Slope ratio is 3:1 favoring X, not Y.

Final answer: D